A Dynamic Market Mechanism for Combined Heat and Power Microgrid Energy Management

Proceedings of the 20th World Congress Proceedings of the 20th World The International Federation of Congress Automatic Control Proceedings of the 20th9-14, World The International Federation of Congress Automatic Control Toulouse, France, July 2017 Available online at www.sciencedirect.com The International of Automatic Control Toulouse, France,Federation July 9-14, 2017 Toulouse, France, July 9-14, 2017

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IFAC PapersOnLine 50-1 (2017) 10033–10039

A Dynamic Market Mechanism for A Dynamic Market Mechanism for A Dynamic Market Mechanism for Combined Heat and Power Microgrid Combined Heat and Power Microgrid Combined Heat Management and Power Microgrid Energy Energy Management Energy Management ∗ ∗∗ ∗∗

Thomas R Nudell ∗ Massimo Brignone ∗∗ Michela Robba ∗∗ ∗∗ Brignone ∗∗ Michela ∗∗ Robba ∗∗ Thomas RAndrea Massimo Nudell ∗∗Bonfiglio Federico ∗∗ Delfino ∗∗ ∗∗ ∗∗ Thomas RAndrea Nudell Bonfiglio Massimo ∗∗ Brignone ∗∗ Robba ∗ Michela Federico Delfino Annaswamy ∗∗ ∗∗ ∗ AndreaAnuradha Bonfiglio Federico Delfino Anuradha Annaswamy ∗∗ Anuradha Annaswamy ∗ Massachusetts Institute of Technology, Cambridge, MA 02139 USA ∗ ∗ Massachusetts Institute of Technology, Cambridge, MA 02139 USA (email:{nudell, aanna}@mit.edu) ∗ Massachusetts Institute of Technology, Cambridge, MA 02139 USA ∗∗ (email:{nudell, aanna}@mit.edu) University of Genoa, Genoa, Italy (email: {massimo.brignone, ∗∗ (email:{nudell, aanna}@mit.edu) ∗∗ University of Genoa, Genoa, Italy (email: {massimo.brignone, michela.robba,a.bonfiglio,federico.delfino}@unige.it) ∗∗ University of Genoa, Genoa, Italy (email: {massimo.brignone, michela.robba,a.bonfiglio,federico.delfino}@unige.it) michela.robba,a.bonfiglio,federico.delfino}@unige.it) Abstract: This paper develops a dynamic market mechanism (DMM) to optimally allocate Abstract: This paper develops a dynamic mechanism (DMM) to optimally allocate electric and thermal power in a combined heatmarket and power microgrid. The market is formulated as Abstract: This paper develops a dynamic market mechanism (DMM) to optimally allocate electric and thermal power in a combined heat and power microgrid. The market is formulated as a receding horizon constrained optimization problem, from which an optimal automated transacelectric andhorizon thermal power in a optimization combined heat and power microgrid. The market is formulated as ative receding constrained problem, from which an optimal automated transacprocedure is developed. The market operation is from distributed in nature and incorporates the a receding horizon constrained optimization problem, which an optimaland automated transactive procedure is developed. The market operation is distributed in nature incorporates the mostprocedure up-to-dateis electric and thermal loadoperation estimatesisand renewable generation. These properties tive developed. market distributed in generation. nature and These incorporates the most up-to-date electric and The thermal load estimates and renewable properties make our microgrid DMM, µDMM, attractive for microgrid energy management systems, as most up-to-date electric and thermal load estimates and renewable generation. These properties make our microgrid DMM, µDMM, attractive for renewable microgrid energy energy resources management systems, as new smart buildings, battery storage systems, and can be added in make our microgrid DMM, µDMM, attractive for renewable microgrid energy energy resources management systems, as new smart buildings, battery storage systems, and can be added in a plug-and-play fashion without reformulating the optimization problem and without adding new smart buildings, battery storage systems, and renewable energy resources can be added in acomputational plug-and-play fashion without reformulating theof optimization problem adding complexity to the EMS. The result the market clearing isand the without spot prices and a plug-and-playcomplexity fashion without reformulating theofoptimization problemis and without adding computational to the EMS. The result the market clearing the spot prices and set-points for electric and thermal power in addition to non-binding estimates of future prices computational complexity to the EMS. The of the market clearing is the of spot prices and set-points for electric and thermal power inis result addition toonnon-binding estimates future prices and set-points. The the market mechanism simulated a CHP Microgrid model based on the set-points for electric and thermal power in addition to non-binding estimates of future prices and set-points. The theMicrogrid market mechanism is simulated on a CHP Microgrid model based on the Smart Polygeneration (SPM) located on the University of Genoa’s Savona campus. and set-points. The theMicrogrid market mechanism is simulated a CHP Microgrid model based on the Smart Polygeneration (SPM) located on the on University of Genoa’s Savona campus. Smart Microgrid (SPM) located Control) on the University of Genoa’s Savona © 2017,Polygeneration IFAC (International Federation of Automatic Hosting by Elsevier Ltd. All rightscampus. reserved. Keywords: Microgrid, combined heat and power, transactive control, dynamic market Keywords: combined heat and power, transactive control, dynamic market mechanism Microgrid, Keywords: Microgrid, combined heat and power, transactive control, dynamic market mechanism mechanism 1. INTRODUCTION Historically, microgrid EMS have been implemented by 1. INTRODUCTION Historically, microgrid (see EMSShahidehpour have been implemented by centralized controllers and Khodayar 1. INTRODUCTION Historically, microgrid (see EMSShahidehpour have been implemented by centralized controllers and Khodayar Centralized control is a reasonable and often The adoption of microgrids is increasing exponentially (2013)). centralized controllers (see Shahidehpour and Khodayar Centralized control a reasonable and often The adoption of with microgrids is increasing exponentially feasible because the is physical scale and number around the world the primary drivers of making the (2013)). (2013)). solution Centralized control is a reasonable and often The adoption of with microgrids is increasing exponentially feasible solution because the physical scale and number around the world the primary drivers of making the of devices in a microgrid is typically small enough to make grid more resilient, reliable, while simultaneously incorpofeasible solution because the physical scale and number around the world with the primary drivers of making the of devices in a microgrid is typically small enough to make grid more resilient, reliable, while simultaneously incorpocentralized problem tractable. more rating more renewable energy. A popular configuration for the of devices in a microgrid is typicallyAdditionally, small enoughand to make grid more resilient, reliable, while simultaneously incorpothe centralized problem tractable. Additionally, and more rating more renewable energy. A popular configuration for importantly, a centralized control is possible when the microgrids that serve commercial and residential loads is the centralizeda problem tractable. Additionally, and more rating morethat renewable energy. A popular configuration for microgrids serve commercial and residential loads is importantly, centralized control is possible when the microgrid and all of its assets are own and operated by a the so-called combined heat and power (CHP) microgrid, a all centralized control is possible whenby the microgrids that serve commercial and residential loads is importantly, microgrid and of its assets are own and operated a the so-called combined heat and power (CHP) microgrid, single entity, thus making all of the device parameters and which provides both electric power and district heating microgrid and all of its assets are own and operated by a the so-called combined heat and power (CHP) microgrid, single entity, thus making all of the device parameters and which provides both electric power and district heating available to solve theallcentralized control problem. (and often cooling). Because microgrid installations are costs single entity, thus making of the device parameters and which provides both electric power and district heating (and often Because microgrid installations are costs available to solve the centralized control problem. relative newcooling). and primarily behind-the-meter installations, availableoftothe solvecentralized the centralized (and often cooling). Because microgrid installations are costs A challenge EMScontrol is theproblem. plug-andrelative new and primarily behind-the-meter installations, there is new no single ubiquitous control and operation archi- A challengeas of the centralized EMS is are theinstalled. plug-andrelative and primarily behind-the-meter installations, playability new microgrid components A there is no single ubiquitous control and operation archi- A challengeas of the centralized EMS is are theinstalled. plug-andtecture. playability new microgrid components A there is no single ubiquitous control and operation archi- more general way to articulate this limitation is as foltecture. playability as new microgrid components are installed. A more general way to articulate this limitation is as foltecture. lows: centralized energy management systems struggle to Microgrid operation and control is hierarchical (see Guer- more general way to articulate this limitation is as follows: centralized energy management systems struggle to Microgrid and control is hierarchical (see recent Guer- adapt to changing conditions within the microgrid at every rero et al. operation (2011)), although there has been some centralized energy management systems struggle to Microgrid and control is hierarchical (see recent Guer- lows: adapt to changinginstallation conditions within microgrid at every rero etwhich al. operation (2011)), although there has been some timescale—from of new the devices to fluctuating work suggests alternative non-hierarchical control adapt to changing conditions within the microgrid at every rero et al. (2011)), although there has been some recent work which(see suggests non-hierarchical control installation of new devices to fluctuating renewable generation and sudden unpredictable device strategies Dorfleralternative et al. (2014)). A hierarchical ar- timescale—from timescale—from installation of new devices to fluctuating work which(see suggests alternative non-hierarchical control renewable generation and sudden unpredictable device strategies Dorfler et al. (2014)). A hierarchical arfailures. Another limitation of centralized controllers is chitecture includes low-level (primary) control which typrenewableAnother generation and sudden unpredictable device strategies (see Dorfler et al.(primary) (2014)). control A hierarchical ar- failures. limitation of centralized controllers is chitecture includes low-level which typthe ability to incentivize third-party investors in microgrid ically ensures stability and high-level control for optimal Another limitation of centralized controllers is chitecture includes low-level (primary)control control for which typ- failures. the ability to incentivize third-party investors in microgrid ically ensures stability and high-level optimal operation, who may not wish to makeinvestors their detailed device operation of the microgrid (secondary or tertiary control), the ability to incentivize third-party in microgrid ically ensures stability and high-level control for optimal who notavailable wish to make detailed device operation the microgrid (secondary or tertiary control), parameters andmay costs to thetheir central controller. sometimesof referred to as the energy management system operation, operation, who may notavailable wish to make their detailed device operation ofreferred the microgrid (secondary or tertiary control), parameters and costs to the central controller. sometimes to as the energy management system Furthermore, since microgrids are often used to test mod(EMS). Thereferred goal oftothe EMS for a CHP microgrid is to parameters and costs available to the central controller. sometimes as the energy management system Furthermore, since microgrids are often used to test mod(EMS). Theeconomic goal of the EMS for a CHP microgrid is to els also for wider grids, a centralized EMS is not suitable achieve the dispatch of real power and thermal sincegrids, microgrids are often used to test mod(EMS). Theeconomic goal of the EMS for a CHP microgrid is to Furthermore, els also for wider a centralized EMS is not suitable achieve the dispatch of real power and thermal for the emulation of complex systemsEMS such isasnot districts or power over aeconomic specified dispatch time horizon. els also for wider grids, a centralized suitable achieve the of real power and thermal power over a specified time horizon. for theAemulation of complex systemsenergy such asmanagement districts or cities. decentralized market-based for theAemulation of complex systemsenergy such asmanagement districts or power over a specified time horizon. cities. decentralized market-based system can overcome these limitations. cities. decentralized market-based energy management systemAcan overcome these limitations.  This work was supported in part by the NSF initiative, Award no. system can overcome these limitations.

 This work was supported in part by the NSF initiative, Award no. EFRI-1441301.  This work was supported in part by the NSF initiative, Award no. EFRI-1441301. EFRI-1441301. Copyright 10448Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © © 2017 2017, IFAC IFAC (International Federation of Automatic Control) Copyright © 2017 IFAC 10448 Peer review under responsibility of International Federation of Automatic Copyright © 2017 IFAC 10448Control. 10.1016/j.ifacol.2017.08.2040

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Market-based transactive control strategies have been actively developed in the academic literature over the last few years. Of particular relevance are those that develop fast energy markets (FEMs), which are intended to operate faster than a typical ”real-time” energy market, which clears on the order of every 5 minutes. Notably, Kiani and Annaswamy (2014) developed a dynamic market mechanism (DMM) for wholesale energy markets based on the principles of distributed convex optimization and gradient play. It was also shown how the DMM theoretically fit into a broader hierarchical transactive control architecture (see Kiani et al. (2014)). The DMM has been generalized to allow various types of flexible loads and storage devices to act as participants in the real time energy and regulation markets in Knudsen et al. (2016); Garcia et al. (2016). Related market-based optimization methods include Zhang et al. (2015), where the power system model is viewed as a primal-dual gradient system that is then incorporated into the real-time optimal power flow (OPF). The resulting problem solves the optimization problem while ensuring stability of the power system model. We build on these ideas, and develop a DMM specifically for microgrid operation that takes into account futures forecasts, much like a model predictive control (MPC) architecture. Accounting for futures forecasts is necessary when optimizing state-dependent agents, such as battery storage. Related work by Wang et al. (2015) develops a market mechanism within a model predictive control (MPC) framework for a grid-connected microgrid, allowing for futures bidding. The authors use the alternating direction method of multipliers (ADMM) algorithm from Boyd (2010) to create bids/offers and to clear the market. Additionally, they only consider electric power microgrids. In this paper, we develop a gradient descent based DMM for a CHP microgrid. The University of Genova, Savona Campus, Smart Polygeneration Microgrid (SPM) Bracco et al. (2016) has been used to test the developed model and approach. The SPM is a research infrastructure funded (2.4 Me) by the Italian Ministry of Research for microgrids and smart grids that is used for the feeding buildings at the Savona Campus. It is a 3-phase low voltage (400 V line-to-line) “intelligent” distribution system and connects: cogeneration microturbines fed by natural gas, a thermal boiler, a photovoltaic field, a concentrating solar powered (CSP) system equipped with Stirling engines, a H2 O/LiBr absorption chiller with a storage tank, an electrical storage based on NaNiCl2 batteries, and two electric vehicle charging stations. The SPM will be connected to a new low-energy building (SEB) under construction—funded (2.7 Me) by the Italian Ministry of the Environment and Protection of Land and Sea)— which acts as an energy prosumer, being characterized by thermal/electrical loads and power plants (geothermal heat pump, wind mill, photovoltaic, thermal solar panels). The SPM, SEB and buildings are used for simulation of a smart district, and for demonstration of smart city solutions inside a living-lab on a campus scale. The organization of this paper is as follows. Section 2 establishes our notation and formulates the CHP EMS problem. Section 3 develops the µDMM to solve the CHP EMS problem. Section 4 illustrates the µDMM operation through simulations of a model based on the SPM campus

Fig. 1. While at operating interval I, remaining intervals are indexed by K = 1, . . . , NH , where NH = N − I. microgrid. Section 5 concludes the paper with a review of contributions, a discussion on practical implementation of the µDMM, and future directions of this work. 2. PROBLEM STATEMENT The goal of the CHP-EMS is to optimally allocate electric and thermal power set-points at every operating interval over a specified time horizon. This section formulates this multi-period receding horizon optimization problem. First we establish the notation and conventions used throughout the paper. 2.1 Notation The units (or agents) of our CHP microgrid model can be classified by the following sets • • • •

heating units (e.g., gas boilers), H cogeneration units, C storage units (e.g., batteries), S low voltage side of the network connection (sometimes called point of common coupling), N

We define the set of all CHP agents that participate in the CHP market as A  H ∪ C ∪ S ∪ N. (1) The CHP-EMS is a multi-period optimization problem, and the proposed DMM is an iterative algorithm that solves this problem. The horizon may be a day, a hour, or another specified length of time, which is subdivided into N shorter operating intervals. We use three index systems to keep track of the operating interval, the remaining intervals, and the DMM iterations. First, the operating intervals are denoted I = 1, . . . , N ; these indexes are fixed at the beginning of the horizon, and the length of each interval is TI . Second, the remaining operating intervals—from the perspective of the current interval I—are denoted K = 1, . . . , NH , where the number of remaining intervals is NH = N − I. The index K will be particularly important when creating bids and offers for future operating intervals. Third, we index DMM iterations, referred to as negotiations, by k = 1, 2, . . .. Figure 1 visualizes N, NH , I, K, and k. For vector-valued variables, we denote the Kth component by [·]K . We will distinguish between electrical and thermal energy or power quantities using the superscripts {·}e and {·}th , respectively. 2.2 CHP Modeling This section describes the CHP microgrid model including the network assumptions and component models.

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Assumption 1: The CHP microgrid can be modeled as a single bus-bar for electric and thermal power, i.e., ignore electric or thermal power network constraints. This assumption is valid when the microgrid covers a smallenough geographic area and line-losses can be ignored.

for power (i.e., charging). Together, (6) with the rated power constraints imply the following capacity constraints (for any i ∈ S)

Assumption 2: The CHP agents behave rationally and attempt to maximize their profit or utility.

(7b)

xi ∈ [xi , xi ]  −  ηi (wi − wi ), P ei xi = max TK  +  ηi e xi = min (wi − wi ), P i TK

Assumption 3: All CHP agents have the following private information, which they are not obligated to share: (1) an internal decision variable xi ∈ RNH , i ∈ A (2) (2) min and max electric and thermal power capacity e th {P ei , P i } and {P th i , P i }, respectively, for i ∈ A (3) thermal and electric conversion functions ei : RNH → RNH and th : RNH → RNH which map each i unit’s (∀ i ∈ A) decision variable to a quantity of real electric power and thermal power, respectively. We assume that these thermal-electric conversion functions are affine of the form ei (xi ) = dei xi (3a) th th i (xi ) = di xi

(3b)

(4) a multi-period cost curve Ji : RNH → R NH  Ji (xi ) = JiK ([xi ]K )

(4)

K=1

(5) additional machine-specific parameters such as state of charge, charge/discharge efficiencies, etc.

The internal decision variables xi ∈ RNH in Assumption 3.1 are used by the agent to determine their bid/offer for electric and/or thermal power for each interval remaining in the horizon. This decision variable is also used by the agent to ensure that local constraints are not violated. The agent’s minimum and maximum capacity, denoted xi and xi , represent the smallest and largest values the decision variable can take based on the current state. In Assumption 3.3, not all units can produce both electric and thermal power. For units that cannot produce electric power such as boilers ei (xi ) = 0, i ∈ H, and for units that cannot produce thermal power such as storage units and the PCC th i (xi ) = 0, i ∈ S ∪ N . In this paper, we do not consider any additional parameters (Assumption 3.5) for i ∈ C ∪ H ∪ N . Additional parameters in Assumption 3.5 private to storage units i ∈ S include the state of charge (SOC) wi ∈ RNH and charge and discharge efficiencies. Assuming a first difference approximation for the rate of change of SOC, the decision variable for storage units can be expressed as [xi ]K = ηi±

[wi ]K+1 − [wi ]K TK

K = 1, . . . , NH ,

i∈S

(5)

where ηi± > 0 ∈ R are suitable charge and discharge efficiencies. The SOC is also assumed to have bounds wi ∈ [wi , wi ]. These bounds imply that the decision variable xi is constrained  as  ηi− ηi+ (wi − wi ), (wi − wi ) i ∈ S. (6) xi ∈ TK TK We note that xi > 0 indicates offering power to the microgrid (i.e., discharging), while x < 0 indicates bidding

(7a)

(7c)

Assumption 4: the cost functions JiK : R → R in (4) are convex quadratic functions of the form 1 (8) JiK ([xi ]K ) = [ai ]K + [bi ]K [xi ]K + [ci ]K [xi ]2K 2 for i ∈ A and K = 1, . . . , NH . This assumption can be relaxed to differentiable convex functions with no modification of our DMM, which will be developed in Section 3. Further discussion on the form of the cost curve is provided in Section 4. 2.3 Multiperiod Optimization The goal of the CHP microgrid operation is to meet electric and thermal power demands at every operating interval I = 1, . . . , N , at the lowest cost while respecting the components’ local constraints. Formally, we state this problem as  Ji (xi ) (9a) minimize xi ,i∈A

i∈A

subject to

he =Pˆ re + Pˆ le − hth =Pˆ lth − m± i (xi ) ≤ 0





ei (xi ) = 0

(9b)

i∈A

th i (xi ) = 0

(9c)

i∈A

i∈A

(9d)

where h : R → R and h : R → R are the global power balance constraints for each interval, ei : RNH → RNH and th : RNH → RNH map each i unit’s decision variable to a quantity of real electric power : RNH → RNH is an affine and thermal power, m± i representation of the capacity constraints e

NH

NH

th

m+ i (xi ) = xi − xi − mi (xi ) = −xi + xi

NH

NH

(10a) (10b)

Finally, Pˆ re , Pˆ le , Pˆ lth ∈ RNH in (9) are three forecast quantities representing electric renewable generation, electric load, and thermal load, respectively. Elements of the forecast quantities correspond to the forecast of the Kth operating interval. For example, if we are within operating interval I, prior to the start of the DMM negotiations, [Pˆ re ]3 corresponds to the electric renewable forecast at interval I +3. Note that problem (9) has a convex objective function (Assumption 4) and affine or convex equality and inequality constraints (Assumption 1), therefore it is convex. In the next section we develop a dynamic market mechanism that will solve the convex problem (9) over a specified time horizon while respecting the privacy of the market participants.

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In the final phase of market operation, accounts are settled based on the cleared bids, offers, and prices. The settlement phase may occur immediately following the operating interval or after some other specified period of time depending on the settlement rules. Detailed discussion of settlement rules and their implication on transactive control is outside the scope of this paper, but can be found in Garcia et al. (2016). 3.2 Optimal Negotiation Strategy Fig. 2. Different types of devices send negotiated bids/offers to a centralized market operator (labeled µDMM) and receive negotiated prices in return. 3. COMBINED HEAT AND POWER DYNAMIC MARKET MECHANISM

The objective of the individual agents in the market is to maximize their own profits, while the objective of the energy management system is to balance thermal and electric power at the lowest possible cost. This section describes a negotiation procedure that results in profitmaximizing bids/offers by the market participants and minimum-cost power allocation.

The DMM formulated here follows closely to the previously developed DMMs in Kiani and Annaswamy (2014); Knudsen et al. (2016). The major differences include the additional thermal power constraints and the futures negotiations, which correspond to remaining intervals K > 1 (right of the break in Fig. 1). We first describe the market rules, which describe how negotiations are made and how the market is cleared. Then we develop an optimal bidding strategy, which dictates how market participants will negotiate.

where the slack variables λe ∈ RNH and λth ∈ RNH represent the price of electric power and thermal power, respectively. The slack variables µ± i ∈ R, i ∈ A represent the internal penalty for violating the capacity constraints (9d).

3.1 Market Rules

The gradient of (13) with respect to xi , i ∈ A is

To begin, we formulate the Lagrangian of (9) as   L0 (x, λ, µ) =

i∈A

e T th Ji (xi ) + λT − e h + λth h

T ± (µ± i ) mi

i∈A



(13)

T

The market operation is split into three distinctive phases: negotiation, market clearing, and settlement phases. The first is a negotiation phase, which occurs before the operating interval. For example, the negotiations for interval I = 2 occur within operating interval I = 1. The automated negotiation process attempts to solve the problem (9) for all remaining intervals. At the start of the negotiation phase, the microgrid units register with market operator, indicating that they wish to participate in the market. Next, the market participants negotiate bids or offers through the market operator. Ideally, each negotiation step should successively improve a unit’s bid or offer. As shown in Fig. 1 negotiation steps are indexed by k. Bids and offers are not binding during the negotiation phase. Figure 2 shows the interaction between the market operator and the microgrid units i ∈ A for the first phase of market operation. The market is cleared in the next phase. Market clearing occurs when the negotiations have reached a steady-state or the maximum number of negotiations have occurred— which ever comes first. The spot value of the cleared bid/offer is binding, while all futures values will be considered non-binding. For example, if unit i ∈ A has the cleared offer xci ∈ RNH , then [xci ]1 becomes binding and will be used to create thermal and/or electric set-point(s): (11) Pie,sp = ei ([xci ]1 ) c (12) Pith,sp = th i ([xi ]1 ) K = 2, . . . , NH , are non-binding indications All of interest, sometimes referred to as advisory set-points. Note that the dimension of the decision variable xi is proportional to NH = N − I, which decreases from length N before the first interval to length 1 before the last operating interval.

[xci ]K ,

∇xi L0 =∇xi Ji (xi ) + [∇xi he ] λe T T ±   + ∇xi hth λth − ∇xi m± µi i where ∇xi Ji (xi ) ∈ RNH [∇xi he ]T = [−∇xi e ]T ∈ RNH ×NH

[∇xi hth ]T = [−∇xi th ]T ∈ RNH ×NH T [∇xi m± i ]

T

(14) (15a) (15b) (15c)

NH ×NH

= diag [±1] ∈ R (15d) It is important to notice that apart from the global electric and thermal pricing information λe and λth , all of the terms in (14) are local to individual units. This gradient information will be used to negotiate the optimal bid or offer. Before stating the negotiation update steps, we make some simplifications based on the assumptions in Section 2. We have assumed that the cost curves Ji (xi ) are quadratic, hence (15a) simplifies to ∇xi Ji (xi ) = bi + diag [ci ] xi (16) We have assumed that the electric and thermal output functions ei and th are affine, hence (15b) and (15c) i simplify to, respectively, [−∇xi e ]T = −diag [dei ] (17a)  th  th T [−∇xi  ] = −diag di (17b)

Given the latest pricing information λke , the gradient-based decision variable update iterate for unit i ∈ A can be written as   xk+1 = xki − αxi i = xki − αxi



∇xi Ji (xki ) + [∇xi he ]T λke − [∇xi hth ]T λkth ∓ µ± i





bi + ci xki − diag [dei ] λke − diag dth λkth ∓ µ± i i

k

k



(18)

where αxi ∈ R is a positive step-size parameter. The local penalty function updates can be computed as

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µ± i

k+1

  k k = max 0, µ± + αµi m± i (xi )

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(19)

where αµi ∈ R is a positive step-size parameter, and max{·} is an element-wise comparison. Each market participant uses the iterates (18) to form electric and thermal k power negotiation bids/offers from ei (xki ), th i (xi ). We note that this need not (or may not) be the case in practice. The market operator collects these bids/ offers then updates the negotiation price of electric and thermal power:    = λke + αλe Pˆ re + Pˆ le − ei (20a) λk+1 e λk+1 th

=

λkth

+ αλth

i∈A



Pˆ lth −



i∈A

th i



(20b)

where αλe , αλth ∈ R are positive step-size parameters.

To summarize, the µDMM starts at the beginning of each operating interval with updated forecasts of Pˆ re , Pˆ le , Pˆ lth ∈ RNH and initial values for the decision variables x0i ∈ RNH , i ∈ A and prices λ0e , λ0th ∈ RNH . The market participants i ∈ A update their decision variables according to (18), and use the resulting value to construct electric and thermal negotiation bids/offers. The bids/offers are Fig. 3. A schematic of the SPM submitted to the market operator, who updates the nego4. SIMULATION tiated prices according to (20). These prices are broadcast to the market participants, and the negotiations continue. The Smart Polygeneration Microgrid (SPM) is an operational CHP microgrid on the University of Genoa’s Savona In (18)–(20), the step-size parameters play an important Campus in Savona, Italy. Extensive physical and cost modrole in the performance of the automated market: if the eling has been done on the SPM (see Bonfiglio et al. (2013), step-size parameters are too small the negotiations will Bracco et al. (2015a), Bracco et al. (2015b), Barillari et al. not converge fast enough and the market may clear at a (2015), Bonfiglio et al. (2012) for details). Figure 3 shows sub-optimal solution, and if the step-sizes are too large a schematic of the SPM. We created a simplified model of the market may oscillate or even become unstable. The the SPM which satisfies the assumptions made in Section 2 following theorem (proof omitted) formalizes this idea. to illustrate our proposed DMM. We describe the model Theorem 1. Assume that the problem (9) is feasible and first, then present the simulation results. there exists an optimal solution {x∗i , λ∗e , λ∗th }, then there exist positive step-size parameters αxi , αµi , i ∈ 4.1 SPM Model A and αλe , αλth such that the iterations (18)–(20) are asymptotically stable. This solution is unique and optimal. The goal of the SPM is to be an efficient, extensible, and resilient combined heat and power microgrid serving The µDMM negotiation phase (18)–(20) continues until the electric and thermal power demands of the Savona the market clears, i.e. when ∇L0  < , for a small  > 0, campus. The SPM units that will participate in the µDMM or if maximum amount of time has elapsed. We denote described in Section 3 are: the cleared values as {xci , λce , λcth } and note that these • low voltage side of the distribution network connecmay differ from optimal solution if the negotiations do not tion, referred to as point of common coupling (PCC) converge in time. The spot prices are used to determine • boiler system rated at about 1000 kW of thermal market settlements, which are not discussed in this paper. power The futures values K = 2, . . . , NH are used to create initial • cogenerator unit rated at 45 kW electric (Cogen 1) bids or offers for the next negotiation phase as • cogenerator unit rated at 65 kW electric (Cogen 2) 0 c xi = [xi ]K , K = 2, . . . , NH , i ∈ A (21a) • storage system consisting of one NaNiCl2 battery (21b) λ0e = [λce ]K , λ0th = [λcth ]K , K = 2, . . . , NH with 141 kWh of capacity. Recall that the dimension of the decision variables is Each agent has a quadratic convex cost function JiK proportional to the number of remaining intervals in the which we assume is fixed for all K = 1, . . . , NH . Table 1 time horizon, NH , which decreases by one after each summarizes the private physical and economic parameters operating interval in our receding horizon formulation. In for each unit i ∈ A that participates in the µDMM, c addition, storage units will use the spot values [xi ]1 , i ∈ S including the rated capacity and electric and thermal to update future state of charge estimates as conversion functions ei (xi ) and th i (xi ), and cost function. c wi = [wi ]K>1 − TI [xi ]1 1NH −1 i ∈ S (22) In addition to these controllable agents, the SPM also has We simulated this µDMM in a microgrid model based on installed photovoltaic panels and concentrated solar power with a combined rated capacity of 83 kW, referred to for the SPM, described in the next section. 10452

Proceedings of the 20th IFAC World Congress 10038 Thomas R Nudell et al. / IFAC PapersOnLine 50-1 (2017) 10033–10039 Toulouse, France, July 9-14, 2017

Name PCC Boiler Cogen 1 Cogen 2 Storage

Rated Capacity (thermal/electric) 1000 kW (e) 1000 kW (th) 45 kW (e) 65 kW (e) 141 kWh (e)

Electricity Production ei (x) x 0 x x x

Thermal Production th i (x) 0 x 2.88x 2.00x 0

Cost Curve JiK (x) 0.0347x + 0.000037x2 0.0947x + 0.001x2 0.7104x + 0.0117x2 0.4755x + 0.0055x2 0.15x + 0.0051x2

Table 1. Summary of SPM agent parameters

Fig. 4. Electric load (blue) and PV production (green)

Fig. 6. Dispatched set-points for the boiler system

Fig. 5. Thermal load for each operating interval

Fig. 7. Dispatched set-points for Cogen 1

simplicity as PV. We assume that no electric and thermal loads in SPM controlable. The simulation time horizon is one day with operating intervals TI = 15 minutes, hence the initial number of operating periods is N = 96. We use PV and electric and thermal load data collected from the Savona campus on July 15, 2015, shown in Fig. 4 and Fig. 5, respectively. 4.2 Results Figures 6–10 show the dispatched power set-points ei ([xci ]1 ) c and th i ([xi ]1 ) for each operating period I = 1, . . . , 96. The market cleared for each operating period, hence the worstcase electric and thermal errors are both on the order of 10−5 kW. In this paper we have omitted the negotiation trajectory of the µDMM due to space limitation. 5. CONCLUSIONS In this paper we developed a µDMM for a CHP microgrid that optimally allocates both electric and thermal power set-points to microgrid agents according to the most up-to-date load and renewable forecasts. The µDMM is attractive to microgrid operators because of the plug-andplay ability to incorporate new devices into the EMS.

Fig. 8. Dispatched set-points for Cogen 2 Another attractive feature is the opportunity to allow third-party investment in the microgrid while respecting the privacy of generator owners. The µDMM use gradient-based bid and offer update rules and assumes that agents have continuous convex cost curves. Market negotiations are conducted over a specified time horizon, and only the next operating period (spot market) is considered binding. The multi-period

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Fig. 9. Expected power production for PCC (positive indicates purchase from the external network)

Fig. 10. Dispatched set-points for the battery system (positive for discharging, negative for charging) optimization formulation is required to optimally operate storage devices. Simulations based on the SPM Campus microgrid model illustrate the operation of our DMM over the course of a day. Future work will include developing bid/offer update rules for non-convex cost curves, such as the piecewise-linear concave cost curves of the actual cogeneration units in the SPM. In addition, future work will analyze the impact of forecast errors and the effectiveness of implementing advanced forecasting algorithms alongside the µDMM. REFERENCES Barillari, L., Bracco, S., Brignone, M., Delfino, F., Pampararo, F., Pacciani, C., Procopio, R., Rossi, M., and Nilberto, A. (2015). An equivalent electric circuit for the thermal Network of the Savona Campus Smart Polygeneration Microgrid. In PowerTech, 2015 IEEE Eindhoven, 1–6. IEEE. Bonfiglio, A., Delfino, F., Pampararo, F., Procopio, R., Rossi, M., and Barillari, L. (2012). The smart polygeneration microgrid test-bed facility of Genoa University. In 2012 47th International Universities Power Engineering Conference (UPEC), 1–6. IEEE. Bonfiglio, A., Barillari, L., Brignone, M., Delfino, F., Pampararo, F., Procopio, R., Rossi, M., Bracco, S., and Robba, M. (2013). An optimization algorithm for the operation planning of the university of genoa smart polygeneration microgrid. In Bulk Power System Dynamics and Control - IX Optimiza-

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tion, Security and Control of the Emerging Power Grid (IREP), 2013 IREP Symposium, 1–8. doi: 10.1109/IREP.2013.6629397. Boyd, S. (2010). Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends in Machine Learning, 3(1), 1–122. doi:10.1561/2200000016. Bracco, S., Brignone, M., Delfino, F., and Procopio, R. (2015a). An Energy Management System for the Savona Campus Smart Polygeneration Microgrid. IEEE Systems Journal, 1–11. doi:10.1109/JSYST.2015.2419273. Bracco, S., Delfino, F., Pampararo, F., Robba, M., and Rossi, M. (2015b). A Dynamic Optimization-based Architecture for Polygeneration Microgrids with TriGeneration, Renewables, Storage Systems and Electrical Vehicles. Energy Conversion and Management, 96, 511– 520. doi:10.1016/j.enconman.2015.03.013. Bracco, S., Delfino, F., Pampararo, F., Robba, M., and Rossi, M. (2016). A Pilot Facility for Analysis and Simulation of Smart Microgrids Feeding Smart Buildings. Renewable and Sustainable Energy Reviews, 58, 1247– 1255. doi:10.1016/j.rser.2015.12.225. Dorfler, F., Simpson-Porco, J., and Bullo, F. (2014). Breaking the hierarchy: Distributed control & economic optimality in microgrids. arXiv preprint arXiv:1401.1767. Garcia, M., Nudell, T.R., and Annaswamy, A.M. (2016). A dynamic regulation market mechanism for improved financial settlements. In 2017 American Control Conference. Submitted. Guerrero, J.M., Vasquez, J.C., Matas, J., de Vicuna, L.G., and Castilla, M. (2011). Hierarchical control of droop-controlled AC and DC microgrids–a general approach toward standardization. IEEE Transactions on Industrial Electronics, 58(1), 158–172. doi: 10.1109/TIE.2010.2066534. Kiani, A. and Annaswamy, A. (2014). A dynamic mechanism for wholesale energy market: Stability and robustness. IEEE Transactions on Smart Grid, 5(6), 2877– 2888. doi:10.1109/TSG.2014.2320954. Kiani, A., Annaswamy, A., and Samad, T. (2014). A hierarchical transactive control architecture for renewables integration in smart grids: Analytical modeling and stability. IEEE Transactions on Smart Grid, 5(4), 2054–2065. doi:10.1109/TSG.2014.2325575. Knudsen, J., Hansen, J., and Annaswamy, A.M. (2016). A dynamic market mechanism for the integration of renewables and demand response. IEEE Transactions on Control Systems Technology, 24(3), 940–955. doi: 10.1109/TCST.2015.2476785. Shahidehpour, M. and Khodayar, M. (2013). Cutting campus energy costs with hierarchical control: The economical and reliable operation of a microgrid. IEEE Electrification Magazine, 1(1), 40–56. doi: 10.1109/MELE.2013.2273994. Wang, T., O’Neill, D., and Kamath, H. (2015). Dynamic Control and Optimization of Distributed Energy Resources in a Microgrid. IEEE Transactions on Smart Grid, 6(6), 2884–2894. doi:10.1109/TSG.2015.2430286. Zhang, X., Li, N., and Papachristodoulou, A. (2015). Achieving real-time economic dispatch in power networks via a saddle point design approach. In Power & Energy Society General Meeting, 2015 IEEE, 1–5. IEEE.

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